Large Language Models (LLMs) are effective at deceiving, when prompted to do so. But under what conditions do they deceive spontaneously? Models that demonstrate better performance on reasoning tasks are also better at prompted deception. Do they also increasingly deceive spontaneously in situations where it could be considered rational to do so? This study evaluates spontaneous deception produced by LLMs in a preregistered experimental protocol using tools from signaling theory. A range of proprietary closed-source and open-source LLMs are evaluated using modified 2x2 games (in the style of Prisoner's Dilemma) augmented with a phase in which they can freely communicate to the other agent using unconstrained language. This setup creates an opportunity to deceive, in conditions that vary in how useful deception might be to an agent's rational self-interest. The results indicate that 1) all tested LLMs spontaneously misrepresent their actions in at least some conditions, 2) they are generally more likely to do so in situations in which deception would benefit them, and 3) models exhibiting better reasoning capacity overall tend to deceive at higher rates. Taken together, these results suggest a tradeoff between LLM reasoning capability and honesty. They also provide evidence of reasoning-like behavior in LLMs from a novel experimental configuration. Finally, they reveal certain contextual factors that affect whether LLMs will deceive or not. We discuss consequences for autonomous, human-facing systems driven by LLMs both now and as their reasoning capabilities continue to improve.

Multi-agent reinforcement learning (MARL) methods, while effective in zero-sum or positive-sum games, often yield suboptimal outcomes in general-sum games where cooperation is essential for achieving globally optimal outcomes. Matrix game social dilemmas, which abstract key aspects of general-sum interactions, such as cooperation, risk, and trust, fail to model the temporal and spatial dynamics characteristic of real-world scenarios. In response, our study extends matrix game social dilemmas into more complex, higher-dimensional MARL environments. We adapt a gridworld implementation of the Stag Hunt dilemma to more closely match the decision-space of a one-shot matrix game while also introducing variable environment complexity. Our findings indicate that as complexity increases, MARL agents trained in these environments converge to suboptimal strategies, consistent with the risk-dominant Nash equilibria strategies found in matrix games. Our work highlights the impact of environment complexity on achieving optimal outcomes in higher-dimensional game-theoretic MARL environments.

Large Language Models (LLMs) have been increasingly used in real-world settings, yet their strategic abilities remain largely unexplored. Game theory provides a good framework for assessing the decision-making abilities of LLMs in interactions with other agents. Although prior studies have shown that LLMs can solve these tasks with carefully curated prompts, they fail when the problem setting or prompt changes. In this work we investigate LLMs' behaviour in strategic games, Stag Hunt and Prisoner Dilemma, analyzing performance variations under different settings and prompts. Our results show that the tested state-of-the-art LLMs exhibit at least one of the following systematic biases: (1) positional bias, (2) payoff bias, or (3) behavioural bias. Subsequently, we observed that the LLMs' performance drops when the game configuration is misaligned with the affecting biases. Performance is assessed based on the selection of the correct action, one which agrees with the prompted preferred behaviours of both players. Alignment refers to whether the LLM's bias aligns with the correct action. For example, GPT-4o's average performance drops by 34% when misaligned. Additionally, the current trend of "bigger and newer is better" does not hold for the above, where GPT-4o (the current best-performing LLM) suffers the most substantial performance drop. Lastly, we note that while chain-of-thought prompting does reduce the effect of the biases on most models, it is far from solving the problem at the fundamental level.

This paper investigates the strategic decision-making capabilities of three Large Language Models (LLMs): GPT-3.5, GPT-4, and LLaMa-2, within the framework of game theory. Utilizing four canonical two-player games -- Prisoner's Dilemma, Stag Hunt, Snowdrift, and Prisoner's Delight -- we explore how these models navigate social dilemmas, situations where players can either cooperate for a collective benefit or defect for individual gain. Crucially, we extend our analysis to examine the role of contextual framing, such as diplomatic relations or casual friendships, in shaping the models' decisions. Our findings reveal a complex landscape: while GPT-3.5 is highly sensitive to contextual framing, it shows limited ability to engage in abstract strategic reasoning. Both GPT-4 and LLaMa-2 adjust their strategies based on game structure and context, but LLaMa-2 exhibits a more nuanced understanding of the games' underlying mechanics. These results highlight the current limitations and varied proficiencies of LLMs in strategic decision-making, cautioning against their unqualified use in tasks requiring complex strategic reasoning.

In social psychology, Social Value Orientation (SVO) describes an individual's propensity to allocate resources between themself and others. In reinforcement learning, SVO has been instantiated as an intrinsic motivation that remaps an agent's rewards based on particular target distributions of group reward. Prior studies show that groups of agents endowed with heterogeneous SVO learn diverse policies in settings that resemble the incentive structure of Prisoner's dilemma. Our work extends this body of results and demonstrates that (1) heterogeneous SVO leads to meaningfully diverse policies across a range of incentive structures in sequential social dilemmas, as measured by task-specific diversity metrics; and (2) learning a best response to such policy diversity leads to better zero-shot generalization in some situations. We show that these best-response agents learn policies that are conditioned on their co-players, which we posit is the reason for improved zero-shot generalization results.

Coordination is often critical to forming prosocial behaviors -- behaviors that increase the overall sum of rewards received by all agents in a multi-agent game. However, state of the art reinforcement learning algorithms often suffer from converging to socially less desirable equilibria when multiple equilibria exist. Previous works address this challenge with explicit reward shaping, which requires the strong assumption that agents can be forced to be prosocial. We propose using a less restrictive peer-rewarding mechanism, gifting, that guides the agents toward more socially desirable equilibria while allowing agents to remain selfish and decentralized. Gifting allows each agent to give some of their reward to other agents. We employ a theoretical framework that captures the benefit of gifting in converging to the prosocial equilibrium by characterizing the equilibria's basins of attraction in a dynamical system. With gifting, we demonstrate increased convergence of high risk, general-sum coordination games to the prosocial equilibrium both via numerical analysis and experiments.

Recent work on promoting cooperation in multi-agent learning has resulted in many methods which successfully promote cooperation at the cost of becoming more vulnerable to exploitation by malicious actors. We show that this is an unavoidable trade-off and propose an objective which balances these concerns, promoting both safety and long-term cooperation. Moreover, the trade-off between safety and cooperation is not severe, and you can receive exponentially large returns through cooperation from a small amount of risk. We study both an exact solution method and propose a method for training policies that targets this objective, Accumulating Risk Capital Through Investing in Cooperation (ARCTIC), and evaluate them in iterated Prisoner's Dilemma and Stag Hunt.

In the future, artificial learning agents are likely to become increasingly widespread in our society. They will interact with both other learning agents and humans in a variety of complex settings including social dilemmas. We consider the problem of how an external agent can promote cooperation between artificial learners by distributing additional rewards and punishments based on observing the learners' actions. We propose a rule for automatically learning how to create right incentives by considering the players' anticipated parameter updates. Using this learning rule leads to cooperation with high social welfare in matrix games in which the agents would otherwise learn to defect with high probability. We show that the resulting cooperative outcome is stable in certain games even if the planning agent is turned off after a given number of episodes, while other games require ongoing intervention to maintain mutual cooperation. However, even in the latter case, the amount of necessary additional incentives decreases over time.